covering system | residue system

A set of numbers a_0, a_1, ..., a_(m - 1) (mod m) form a complete set of residues, also called a covering system, if they satisfy a_i congruent i (mod m) for i = 0, 1, ..., m - 1. For example, a complete system of residues is formed by a base b and a modulus m if the residues r_i in b^i congruent r_i (mod m) for i = 1, ..., m - 1 run through the values 1, 2, ..., m - 1.

congruence | exact covering system | multiplicative order | reduced residue system | residue class